The Capital Asset Pricing Model

By Jeffrey S. Coons; PhD, CFA

By Christopher J. Cummings; CFA, CFP™

While Dr. Harry Markowitz is credited with developing the framework for constructing investment portfolios based on the risk-return tradeoff, William Sharpe, John Lintner, and Jan Mossin are credited with developing the Capital Asset Pricing Model (CAPM). 

Introduction

CAPM is an economic model based upon the idea that there is a single portfolio representing all investments (i.e., the market portfolio) at the point of the optimal portfolio on the CML and a single source of systematic risk, beta, to that market portfolio.   The resulting conclusion is that there should be a “fair” return physician investors should expect to receive given the level of risk (beta) they are willing to assume. 

Thus, the excess return, or return above the risk-free rate, that may be expected from an asset is equal to the risk-free return plus the excess return of the market portfolio times the sensitivity of the asset’s excess return to the market portfolio excess return.

Beta then, is a measure of the sensitivity of an asset’s returns to the market as a whole.  A particular security’s beta depends on the volatility of the individual security’s returns relative to the volatility of the market’s returns, as well as the correlation between the security’s returns and the markets returns. 

Thus, while a stock may have significantly greater volatility than the market, if that stock’s returns are not highly correlated with the returns of the overall market (i.e., the stock’s returns are independent of the overall market’s returns) then the stock’s beta would be relatively low.

A beta in excess of 1.0 implies that the security is more exposed to systematic risk than the overall market portfolio, and likewise, a beta of less 1.0 means that the security has less exposure to systematic risk than the overall market.

The CAPM uses beta to determine the Security Market Line or SML.  The SML determines the required or expected rate of return given the security’s exposure to systematic risk, the risk-free rate, and the expected return for the market as a whole. The SML is similar in concept to the Capital Market Line, although there is a key difference. 

Both concepts capture the relationship between risk and expected returns.

However, the measure of risk used in determining the CML is standard deviation, whereas the measure of risk used in determining the SML is beta.  

Conclusion 

The CML estimates the potential return for a diversified portfolio relative to an aggregate measure of risk (i.e., standard deviation), while the SML estimates the return of a single security relative to its exposure to systematic risk. 

Now, if this is the essence of the Capital Asset Pricing Model, what are the arguments against CAPM?

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Filed under: Portfolio Management | Tagged: Investing Basics | 2 Comments »

Portfolio Management 

By Jeffrey S. Coons; PhD, CFA

By Christopher J. Cummings; CFA, CFP™

Modern Portfolio Theory (MPT) is the basic economic model that establishes a linear relationship between the return and risk of an investment.  The tools of MPT are used as the basis for the passive asset mix, which involves setting a static mix of various types of investments or asset classes and rebalancing to that allocation target on a periodic basis.  

Introduction

According to MPT, when building a diversified investment portfolio, the goal should be to obtain the highest expected return for a given level of risk.  A key assumption underlying modern portfolio theory is that higher risk generally translates to higher expected returns.

From the perspective of MPT, risk is defined simply as the variability of an investment’s returns.  While MPT is based upon the idea that expected volatility of returns is used, risk is measured by standard deviation of historical returns in practice. 

Standard deviation is a measure of the dispersion of a security’s returns, X₁,…,X_n, around its mean (or average) return.   

Often, standard deviation is calculated using monthly or quarterly data points, but is represented as an annualized number to correspond with annualized returns of various investments.  

Now, let us assume Stock A has a mean return of 10.0 percent and a standard deviation of 7.5 percent. 

Then, approximately 68 percent of Stock A’s returns are within one standard deviation of the mean return, and 95 percent of Stock A’s returns are within 2 standard deviations.

In other words, 68 percent of Stock A’s returns should be between 2.5 percent and 17.5 percent, and 95 percent of the returns for Stock A should be between negative 5.0 percent and 25.0 percent. 

However, a key assumption underlying this logic is that the returns for Stock A are normally distributed (i.e., including that the distribution curve of Stock A’s returns is symmetrical around the mean).

Unfortunately, in reality security returns may not be symmetrically distributed and both the mean return and standard deviation of returns may shift dramatically over time. 

Sources of Risk 

There are many different sources of risk, but the two forms of risk hypothesized by Harry Markowitz Ph.D., father of MPT, were systematic risk and unsystematic risk.

Systematic risk is sometimes referred to as non-diversifiable risk, since it affects the returns on all investments.  

In alternate theories like the Capital Asset Pricing Model [CAPM], systematic risk is defined as sensitivity to the overall market. While Arbitrage Pricing Theory has several common macroeconomic and market factors that are considered sources of systematic risk.   

Investors are generally unable to diversify systematic risk, since they cannot reduce their portfolio’s exposure to systematic risk by increasing the number of securities in their portfolio. 

In contrast, physicians diversifying an investment portfolio can reduce unsystematic risk, or the risk specific to a particular investment.  Sources of unsystematic risk include a stock’s company-specific risk and industry risk. 

For example, in addition to the risk of a falling stock market, physician investors in Merck also are exposed to risks unique to the pharmaceutical industry (e.g., healthcare reform), as well as the risks specific to Merck’s business practices (e.g., success of research and development efforts, patent time frames, etc). 

Assessment

A physician investor can reduce unsystematic risk by building a portfolio of securities from numerous industries, countries, and even asset classes.  

Thus, portfolio risk in MPT refers to the both systematic (non-diversifiable) and non-systematic (diversifiable) risk, but a basic conclusion of MPT is that no investor would be rational to take on non-systematic risk since this risk can be diversified away.

Conclusion 

MPT is the philosophy that higher returns correspond to higher risk, and that doctor investors typically desire to earn the highest return per a given level of risk.

The tradeoff between expected return and volatility of returns to make investment decisions is known as the mean-variance framework and is central concept in many of today’s passive asset allocation portfolio management principles. 

Now, is MPT as viable today – as when it was originally proposed?

Conclusion

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Filed under: Portfolio Management | Tagged: Investing Basics | 1 Comment »